Carmen Molina-Paris (School of Mathematics, University of Leeds, Leeds, UK & Los Alamos National Laboratory, Los Alamos, New Mexico, USA)

"A Story Of Co-infection, Co-transmission and Co-feeding: How To Compute an Invasion Reproduction Number - A Deterministic Analysis"

Abstract: In this seminar I aim to show you what happens to a theoretical physicist, who gets to work in Theoretical Immunology and Virology. During the journey the physicist gets to learn mathematics she did not know at the time, and of course, explores the biological universe at different scales. Since we only have a limited amount of time, I would like to introduce you to a problem that I have recently become interested in, and which has received NIH funding.

Co-infection of a single host by different pathogens is ubiquitous in nature [1]. We consider a population of hosts (e.g., small or large vertebrates) and a population of ticks, both of them susceptible to infection with two different strains of a given virus. We note that for the purposes of our models, we have Crimean-Congo hemorrhagic fever virus (a segmented Bunyavirus) in mind, as the application system. First, we focus on the dynamics of a single infection, proposing a deterministic model to understand the role of co-feeding in the transmission of the virus. We then compute the basic reproduction number by making use of the next generation matrix approach [2].

When considering co-infection by two distinct strains (one resident and one invasive), we make use of differential equations to model the dynamics of susceptible, infected and co-infected species, and we compute the invasion reproduction number of the invasive strain [3]. I discuss some problems with the calculation, and the solution proposed by Samuel Alizon and Marc Lipsitch [3]. I conclude with a perspective on how the co-infection model can be applied to HIV, and plans for future work and work in progress [4].

To end the talk, I would like to showcase a number of problems in immunology I have worked on, and which have required, for instance, the theory of stochastic processes [5], probability generating functions [6], or the use of a Grobner basis [7].

References
[1] Cox, F.E. (2001). Concomitant infections, parasites and immune responses. Parasitology 122: S23–S38. https://doi.org/10.1017/s003118200001698x
[2] Van den Driessche, P. (2017). Reproduction numbers of infectious disease models. Infectious Disease Modelling 2(3): 288–303. https://doi.org/10.1016/j.idm.2017.06.002
[3] Alizon, S. (2013). Co-infection and super-infection models in evolutionary epidemiology. Interface Focus 3: 20130031. https://doi.org/10.1098/rsfs.2013.0031
[4] Allen, L.S. (2010). An Introduction to Stochastic Processes with Applications to Biology. Chapman and Hall/CRC, New York.
[5] Lythe et al. (2016). How many TCR clonotypes does a body maintain? Journal of theoretical biology, 389, 214–224.
[6] Feliciangeli et al. (2022). Why are cell populations maintained via multiple compartments? Journal of the Royal Society Interface, 19, 20220629.
[7] Sta et al. (2023). Algebraic study of receptor-ligand systems: a dose-response analysis. SIAM Journal on Applied Mathematics S105–S150.